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# An automobile engine propels a $1000\ kg$ car $(A)$ along a levelled road at a speed of $36\ km h^{-1}$. Find the power if the opposing frictional force is 100 N. Now, suppose after travelling a distance of $200\ m$, this car collides with another stationary car $(B)$ of same mass and comes to rest. Let its engine also stop at the same time. Now car $(B)$ starts moving on the same level road without getting its engine started. Find the speed of the car $(B)$ just after the collision.

A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

Here, mass of the car A, $m_A=1000\ kg$

Initial speed of car A $u_A=36\ kmh^{-1}=36\times\frac{5}{18}\ m/s=10\ ms^{-1}$

The opposing force of friction $F=100\ N$

So, power of car A, $P_A=Fu_A=100\ N\times10\ ms^{-1}=1000\ W$

**After a collision with car B of the same mass:**

Final speed of car A, $v_A=0$

Final speed of car B, $v_B=0$

On applying conservation of momentum,

$m_Au_A+m_Bu_B=m_Av_A+m_Bv_B$

Or $1000\times10+1000\times0=1000\times0+1000\times v_B$

Or $v_B=\frac{10,000}{1000}=10\ ms^{-1}$

Therefore, the speed of car B after the collision is $10\ ms^{-1}$.

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